A process for hot filling a container with a sterilized liquid, generally at a temperature that is between 60 to 95.degree. C. An embodiment of the process includes (a) providing a container that is made of a polymer and following a process that can make it able to withstand the hot filling of said liquid; (b) filling the container with said hot liquid; (c) closing the filled container immediately after filling; (d) allowing the container to cool at least below a transition temperature that is on the order of from 40.degree. C. to 50.degree. C. and forming a depression inside the container, resulting in visible deformation; and (e) heating the container to bring about a relief of the residual stresses, whereby this relief leads to a shrinkage and consecutively generates an internal pressurization that compensates for at least the deformation undergone by the effects of the depression of stage (d).